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21Metallurgical Science and TechnologyVol. 27-1 - Ed. 2009

Mechanical and microstructural characterisation of A356 castings realised with full and empty cores

Mattia Merlin, Gian Luca GaragnaniDepartment of Engineering, University of Ferrara, Italy

ABSTRACT

The use of full cores, for producingautomotive components by means of thepermanent mould casting technique, allowsgood castings with a low level of defects to beobtained. Nevertheless, an extra phase of theproduction cycle is necessary to have anoptimal emptying of the internal cavities of thecastings, with an increase in costs. Thisscenario motivated the present research, inparticular to study the effect of replacing fullcores with empty cores. The componentanalysed is one of the three parts of amotorcycle frame, realised in aluminum alloyA356 by permanent mould casting and T6heat-treated. Several castings have beenproduced with both full and empty cores;tensile strength tests have been performed onsamples drawn from four different zones, inorder to compare the mechanical andmicrostructural properties of the castingsrealised with the two different kinds of core. Aslight decrease in elongation at fracture hasbeen verified in the samples drawn from thecastings realised with empty cores, but yieldstrength and ultimate tensile strength are wellcomparable. A finer microstructure alwayscorresponds to higher mechanical properties;an inverse correlation between secondarydendrite arm spacing and ultimate tensilestrength has been found. The effect ofsecondary phases, porosities andmorphology and distribution of eutecticsilicon particles has been considered. TheJapanese Taikai methodology has beenimproved in order to compare the currentproduction cycle with the one optimised bythe use of empty cores. Cost, weight and time-cycle reductions in the production of thecomponent, due to the elimination of the extraphase using empty cores, have beenevaluated.

RIASSUNTO

L’utilizzo di anime piene per la realizzazionedi componenti automotive, mediante processodi colata in stampo permanente, consente diottenere getti di buona qualità con un bassolivello di difettosità. Ciononostante, al fine diottenere un completo svuotamento dellecavità interne del getto, è necessaria una fasesupplementare nel ciclo produttivo coninevitabile aumento dei costi. Questo aspettoha motivato la presente attività di ricercasperimentale con lo scopo di studiare l’effettodella sostituzione delle anime piene conanime cave. È stata esaminata una delle treparti di cui è costituito un telaio motociclistico,realizzato in lega A356 con processo dicolata in conchiglia e trattato termicamenteT6. Sono stati prodotti numerosi gettisperimentali mediante l’uso sia di animepiene sia di anime cave e sono state condotteprove di trazione su provini ricavati daquattro diverse zone di ciascun getto; leproprietà meccaniche sono state correlatecon le proprietà microstrutturali per entrambele tipologie di getto. È stata constatata unaleggera diminuzione dell’allungamentopercentuale a rottura sui getti realizzati conanime cave, tuttavia carico di snervamento ecarico di rottura sono risultati perfettamenteconfrontabili. Ad una microstruttura più fine corrispondono migliori proprietàmeccaniche. È stata individuata unacorrelazione inversa tra la distanzainterdendritica secondaria e il carico unitariodi rottura. È stato valutato anche l’effetto dellefasi secondarie, delle porosità e dellamorfologia e distribuzione delle particelle disilicio eutettico. La metodologia giapponeseTaikai è stata applicata con successo sulcomponente in esame, consentendo dicomparare l’attuale ciclo produttivo conquello ottimizzato mediante l’utilizzo dianime cave. L’introduzione di quest’ultime el’eliminazione della fase supplementare disvuotamento consente una riduzione di costi,pesi e tempi-ciclo.

KEYWORDS

A356 alloy, permanent mould castings, sandcores, tensile properties, microstructure.

22 Metallurgical Science and Technology Vol. 27-1 - Ed. 2009

Fig. 1: Rear-frame (courtesy of TFC-Galileo).

INTRODUCTIONIn the automotive field the use of foundryaluminum alloys allows near-net-shapecomponents to be produced, also forstructural applications because of their highstrength-to-weight ratio in heat-treatedconditions. In particular, aluminum-siliconalloys have widespread applications in thefield of transport because of their goodcastability, their corrosion resistance andtheir excellent recycling behaviour.Moreover, technological innovation andthe increased usage of aluminum alloycould reduce emissions and energyconsumption in the automotive sector. Abetter understanding of the relationshipbetween microstructure and mechanicalproperties in cast aluminum-silicon alloyswill improve foundry practice, in particularin those applications in which weightreduction is an important objective.In their research, various authors report theeffect of chemical composition and heattreatment on microstructure [1,2,3]. Also,analytical and empirical models correlatingthe main solidification parameters and thesecondary dendrite arm spacing can befound in literature [4,5]. In A356aluminum-silicon alloy, the secondarydendrite arm spacing (SDAS), the shapeand distribution of eutectic silicon particlesand secondary phases all control thetensile properties of pore-free castings [6].The presence of Fe-rich secondary phasesaffects the mechanical properties of A356alloy, in particular the ductility of the alloy.

The amount and number of Fe-richintermetallics strictly depend on themagnesium content [7,8]. Strontiumadditions and different solidification rateshave a great effect on the microstructure; incast aluminum alloys both yield strength(YS) and ductility are improved by the T6heat treatment, due to the precipitation of fine β'-Mg2Si particles and thespheroidisation of the eutectic siliconparticles [9,10].The aim of this study is to investigate thetensile properties of samples, drawn fromseveral castings produced by thepermanent mould casting technique. Thecomponent analysed is one of the threestructural parts of a motorcycle framerealised in strontium-modified A356 alloy.In current production, the cavities of thecomponent are obtained by means of twofull cores and bulges could develop on thesurface of the component if, during thefollowing T6 heat treatment, only a smallquantity of sand is present. Generally, themechanical vibration of the component atthe exit of the cooling tunnel is not enoughto completely eliminate the sand inside theinternal cavities. Therefore, in order toavoid the presence of bulges, an extraphase in the production cycle – namely“hot flogging” - is necessary to completelyempty the sand.Hot flogging determines an increase in theproduction costs of the component. Thesubstitution of full cores with empty corescould eliminate the hot flogging phase. This

way, less sand has to be eliminated andmechanical vibration is enough tocompletely empty the cavities in thecomponent. Tensile strength tests havebeen performed on samples drawn fromfour different zones of several castingsrealised with full and empty cores in orderto compare their mechanical properties, interms of ultimate tensile strength (UTS), YSand percentage of elongation at fracture(A%). Microstructural features, such asSDAS and eutectic silicon particles, havebeen correlated to mechanical properties.In order to evaluate the presence ofporosities in the castings and also in thesamples, both macro and micro focus X-rayequipment have been used. In addition tometallographic inspections, fractographicanalyses have also been performed on thefractured samples by means of OpticalMicroscopes (OM) and Scanning ElectronMicroscopes (SEM) with Energy DispersiveX-ray Spectroscopy (EDS), with the aim ofdetermining SDAS, the presence ofsecondary phases, gas and shrinkageporosities, and of analysing the fractureprofile and surface. The effect ofmicroconstituents on crack nucleation andpropagation has been evaluated. Allmechanical and microstructural propertiesof the castings obtained with the twodifferent kinds of core have beencompared. The advantage of using emptycores to reduce time and production costshas been quantified by means of theJapanese Taikai methodology.

EXPERIMENTALResearch has been performed onexperimental castings produced to optimisethe properties of the rear component of amotorcycle frame – namely “rear-frame” -obtained by permanent mould casting andshown in Fig. 1. Tensile strength tests havebeen carried out on samples of severalcastings machined from four differentzones, half realised with full cores and halfrealised with empty cores.

ALLOY AND COMPONENTPRODUCTION

The rear-frame castings have beenproduced with A356 alloy, whose wt.%chemical composition is shown in Table 1.

23Metallurgical Science and TechnologyVol. 27-1 - Ed. 2009 Metallurgical Science and Technology

Table 1. Chemical composition of A356 alloy (typical range of element wt.%)

Alloy Si Fe Cu Mn Mg Zn Sn Ni Al

6.97 0.086 0.002 0.003 0.381 0.006 0.001 0.004

A356 ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ Bal.

7.38 0.108 0.003 0.005 0.425 0.009 0.002 0.007

The alloy has been melted in an electric-induction furnace at 740 ± 5°C, thenmodified by adding Al-10%Sr master alloyto achieve the target strontium level of 0.02wt.%. The chemical composition of the alloyhas been analysed by means of OpticalEmission Spectroscopy (OES). The melt hasbeen degassed with nitrogen for 20minutes, using a rotary degasser beforepouring. After solidification andmechanical vibration, only the castings withfull cores have also been submitted to hotflogging, that is a solubilisation at 500°Cfor 480 minutes. Then the T6 heat treatmenthas been carried out on all castings,consisting of solubilisation at 530 ± 5°C for6h, water quenching at 80 ± 5°C andartificially aging at 145 ± 5°C for 6h.

CORES PRODUCTION

The sand cores have been producedstarting from granular sands covered by athermoset resin. The shell mouldingtechnique has been used for producingboth full and empty cores; the sand hasbeen blown on a metal model, pre-heatedat 230°C in order to allow thepolymerisation of the resin. The differencein producing the two types of core is foundin the amount of time the sand remains inthe metal mould. Sand cores are veryexpensive, so they have a great influenceon the production costs. Empty cores in thiscase are on average 45% lighter than fullcores, with advantages in terms ofenvironmental impact and costs.

CNC MEASURES

A tridimensional control unit has been usedto measure all cores and castings and toverify their dimensional tolerances. Thedimensions of the castings have beencontrolled after their solidification as theyexit the cooling tunnel and also at the exitof the heat treatment plant; this way,possible differences with respect to nominaldimensions due to the heat treatment, areevaluated.

TENSILE STRENGTH TESTS AND NON-DESTRUCTIVE TESTS

Tensile samples have been machined fromthe castings in four different zonesaccording to the Japanese norm JIS Z

2241:1998 “Method of tensile test methodfor metallic materials”. The dimensions ofthe samples are reported in Table 2. In Fig.2, two of the four drawing positions of thesamples have been highlighted. In order todistinguish between samples drawn fromcastings obtained by full cores and samplesfrom empty cores, they have been named

Fxy-samples and Exy-samples, respectively.The subscript ‘x’ indicates the number ofthe casting and the subscript ‘y’ indicatesthe position, from 1 to 4. Tensile tests havebeen performed using an ITALSIGMA 20kN testing machine and the mechanicalproperties have been measured accordingto UNI EN 10002-1:2004.

Table 2. Sample dimensions

Over-all length Thickness Width of grip Gage lengthsection

Dimensions[mm] 60 2.5 8 25

Fig. 2: The drawing positions 1 and 2 on the samples.

In order to verify the absence ofmacroscopic defects, macro focus X-rayequipment has been used for a preliminaryanalysis of the castings. Moreover,penetrating liquid tests have been carriedout to control defects communicating withthe external surfaces of the components.Also the tensile samples have beenanalysed by micro focus X-ray equipment,

which can magnify an image several timesoffering more definition than aconventional X-ray tube.

MICROSTRUCTURAL INVESTIGATION

Microstructural analysis has been carriedout on the tested fractured samples, usingOM equipped with image analysis

Vol. 27-1 - Ed. 2009Metallurgical Science and Technology24

software. Average SDAS values have beenobtained by means of the linear interceptmethod. In each specimen, ten randomareas have been acquired over the entiresurface and several measurements havebeen taken, in order to calculate mean values.The fracture profile has been observed onthe prepared metallographic section, cutout perpendicularly to the fracture surface.Important information concerning thefracture mechanism and the microstructuralcomponents involved in the crack has been

obtained. Also the effect of eutectic siliconparticles and secondary phases has beenevaluated.The fracture surfaces have been examinedusing SEM and analysis of the mainprecipitates has been performed by EDS.

TAIKAI METHODOLOGY

Taikai is a Japanese methodology that isuseful in the evaluation of production cyclesas it aims to increase the efficiency of the

process according to the logic ofcontinuous improvement. The method iscomposed of a series of phases. Some ofthese phases analyse the production layoutand economical waste, others can definenew improvement targets. The evaluation ofthe potential advantages, due to thesubstitution of full cores with empty cores inthe production cycle, has been carried out.In particular, the percentage reduction ofweights, costs and the time-cycle has beencalculated.

Fig. 3: Microstructure of a casting realised with full cores: a) position 1, b) position 2.

RESULTS AND DISCUSSION

MICROSTRUCTURAL ANALYSIS

The microstructure of the componentsanalysed consists of a primary phase, α-Alsolid solution, and an eutectic mixture ofaluminum and silicon. The primary phaseprecipitates from the liquid in the form ofdendrites. The addition of strontiumchanges the eutectic silicon aspect ratiofrom acicular to fibrous. Fibrous eutectic

silicon particles improve the mechanicalproperties of cast aluminum-silicon alloys[11]. The microstructure of the castingsrealised, by means of the two differentkinds of core, has been compared in orderto evaluate whether the different thicknessof cores has a role in the microstructuraland mechanical properties of the alloy.

Defects and secondary phases

Typical microstructures of samples drawnfrom the castings obtained by full and

empty cores are reported in Fig. 3 and Fig.4, respectively. Comparing Fig. 3a with Fig.4a and Fig. 3b with Fig. 4b, SDAS valuesare in good agreement with thecorresponding positions. The distribution ofeutectic silicon particles is generallyuniform and globular, as a consequence ofthe modification of the alloy and the heattreatment. Samples taken from positions 1and 4 in castings obtained by means ofempty cores show a distribution of eutecticsilicon particles that is slightly less uniformthan in the other positions.

A) B)


Fig. 4: Microstructure of a casting realised with empty cores: a) position 1, b) position 2.

A) B)

In aluminum-silicon alloys the loss ofductility, shock resistance and machinabilityis usually due to the presence of Fe [12]. Asshown in Fig. 5, Fe-rich intermetallics withtheir typical needle shape and othersecondary phase particles, such as α-Al(Mn,Fe)Si phase with the Chinesescript morphology, have been observed in the specimens analysed [13, 14]. Alsomicroshrinkage and gas porosities havebeen found, in particular an interdendriticcavity is depicted in the micrograph in Fig. 6.

Analysis of the fracture profile

Fracture profiles have been analysed bymeans of OM in order to understand thecrack’s growth and the effect of secondaryphases better. As shown in Fig. 7, the crackcrosses the interdendritic eutectic regionwhere a significant fraction of intermetallicsand eutectic silicon particles can be found.The presence of hard and needle-shapedphases determines high stressconcentration. A large number of crackedsilicon particles and secondary cracksparallel to the principal crack and normalto the tensile stress can be observed in Fig.7 and Fig. 8.

Fig. 5: Optical micrograph showing the presence ofsecondary phases.

Fig. 6: Optical micrograph of shrinkage porosity.

Fig. 7: Optical micrograph of the fracture profile:presence of a secondary crack.

Fig. 8: Optical micrograph of cracked siliconparticles and secondary phases.


SEM analysis of the fracture surfaces

As shown in Fig. 9, SEM analysis of thefracture surfaces of samples, taken fromboth types of casting, reveals atranscrystalline fracture [15]. This kind offracture surface is typical of modifiedaluminum-silicon alloys subjected to T6 heattreatment. Visible traces ofmicrodeformations (dimples) in the α-Alsolid solution can be seen (Fig.10). In Fig.11 the fracture surface reveals that dimpleshave been formed around cracked siliconparticles, as a result of plastic deformation ofthe matrix. Fractures in the two-phase regionwith decohesion on the interface between α-Al and silicon particles have been found.In Fig. 12 the presence of shrinkageporosity on the fracture surface is shown.The path of the crack is interdendritic, i.e.the fracture profile follows theinterdendritic eutectic zone. Gas porositieshave also been observed; the addition ofeither sodium or strontium for themodification of the alloy could increase thehydrogen content and, as a result, thepresence of gas porosities [16].On the fracture surface and in particularinside the shrinkage porosities, thepresence of secondary-phase precipitateshas been observed. Both β-(AlFeSi) andAl(Mg,Fe)Si intermetallic phases havebeen revealed by EDS microprobe [14,15]. In Fig. 13 the SEM micrograph of aAl8Mg3FeSi6 platelet with its EDS spectrumis reported.

Fig. 9: Transcrystalline and ductile fracture. Fig. 10: Microdeformations in the α-Al solid solution.

Fig. 11: Presence of a cracked silicon particle. Fig. 12: Shrinkage porosity and the interdendriticpath of the crack.

Fig. 13: Al8Mg3FeSi6 platelet with its EDS spectrum.


TENSILE TESTING RESULTS

From tensile tests, stress-strain curves havebeen obtained by attaching a knife-edgeextensometer to the gage length. In Fig. 14and Fig. 15 the mean values of UTS and ofYS are shown, which have been obtainedfrom the samples drawn in the fourdifferent positions. The standard deviationsare reported as error bars. UTSs in position2 and position 3 show the highest values,but in all the four regions values areacceptable according to the expectedrange of values. Regardless of the drawingposition, the samples machined from thecastings obtained by empty cores (Exy-samples) show higher YSs than the onesobtained by full cores (Fxy-samples).Notwithstanding, the maximum standarddeviations of Fxy-samples are higher withrespect to standard deviations of Exy-samples.In Fig. 16 the mean values of A%calculated on all samples are reported. Thestandard deviations are very high and onlythe castings obtained by means of full coresare within the project specifications. Thelowest values in Exy-samples are probablydue to the elimination of the hot floggingphase in the production cycle. Castingsrealised by means of empty cores mostlikely need improvement in the heattreatment parameters, in order to increaseductility.Despite this lower A% in Exy-samples, fromdata obtained from tensile tests, it ispossible to conclude that the mechanicalproperties are comparable between the

Fig. 14: Mean values of UTSs. The standard deviations are reported as error bars.

Position 1

350

300

250

200

150

100

UTS

[M

Pa

]

Position 2 Position 3 Position 4

252,37

249,50

279,61

282,39

275,13

262,47

284,54

280,70

Full cores

Empty cores

Fig. 15: Mean values of YSs. The standard deviations are reported as error bars.

Position 1

240

220

200

180

160

140

12

100

YS

[MP

a]


210,55

213,93

211,41

215,35

213,45

215,79

209,81

217,32

Full cores

Empty cores

Fig. 16: Mean values of A%. The standard deviations are reported as error bars.

A%

9,00

8,00

7,00

6,00

5,00

4,00

3,00

2,00

1,00

0,00

[%]

5,43

3,25

Full cores

Empty cores

two different kinds of casting. Also,microstructural analysis has confirmed themain results obtained from mechanicaltests. The ductility of the alloy stronglydepends on the size, morphology anddistribution of eutectic silicon particles. InExy-samples drawn from position 1 and 4,silicon particle distribution is less uniformthan in the other positions, and thisconfirms the lower mean values of A%.


Relationship between tensileproperties and SDAS

In Fig. 17 the SDAS mean values measuredon Fxy-samples and Exy-samples in the fourdifferent positions, are reported; as shownin the diagram, position 1 and 4 presentthe highest values and no significantdifferences among Fxy-samples and Exy-samples SDAS values can be found in thedifferent positions.The tensile properties of each sample, inparticular UTS and YS, are plotted in Fig.18 and Fig. 19 as a function of SDAS.SDAS measurements are correlated totensile strengths with the aim ofinvestigating the microstructural effect onmechanical properties. The results showthat an inverse correlation between UTSand SDAS can be found for both Fxy-samples and Exy-samples; a finermicrostructure corresponds to a higherUTS. Unlike UTS, YS does not significantlydepend on the scale of dendritic structure[6].

TAIKAI ANALYSIS

By means of Taikai methodology, theanalysis of the potential advantages ofsubstituting full cores with empty cores inthe production cycle, has been carried out.In this analysis the reduction of weights,costs and time-cycle in the different phasesof the production cycle with empty cores,with respect to the production cycle with fullcores, has been evaluated. All thisinformation is summarised in Fig. 20 andconsiderable advantages of using emptycores in the production cycle of the rear-frame component can be seen. Inparticular, the elimination of the hotflogging phase because of the use of emptycores determines a remarkable reduction inproduction costs. In Fig. 21 the totalproduction costs have been compared; bymeans of Taikai methodology, a reductionof 9% in costs has been found when usingthe empty cores instead of using the moretraditional full cores.

Fig. 17: Comparison of SDAS mean values in Fxy-samples and Exy-samples. The standard deviations arereported as error bars.

Position 1

60

50

40

30

20

10

0

SDA

S [μ

m]


41

42

34

34

36

38

34

34

Full cores

Empty cores

Fig. 18: Correlation between SDAS and UTS values.

320

300

280

260

240

220

UTS

[MPa

]

Full cores

Empty cores

25 27 29 31 33 37 3935 41 43 45 47 49

SDAS [μm]

Fig. 19: Correlation between SDAS and YS values.

225

220

215

210

205

200

195

190

YS

[MPa

]

Full cores

Empty cores

25 27 29 31 33 37 3935 41 43 45 47 49

SDAS [μm]


Fig. 20: Comparison of weights, times and costs of production with empty and full cores: normalised values.

weig

ht of c

ore k

it

1

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0

cost

of core

kit

weig

ht of r

esin in

core

kit

cost

of low

ering em

issio

n

quantity o

f core

disp

osed o

f

cost

of sand tr

ansport

stress

of c

ores a

nd casti

ngs handlin

g

floggin

g tim

e

cost

of flo

gging

operato

r’s w

aiting ti

me

cost

of opera

tor’s

waiti

ng tim

e

hot flo

gging ti

me

cost

of hot f

loggin

g

satu

ratio

of h

eat tre

atment p

lant

Full cores Empty cores

Fig. 21: Comparison of production costs with empty and full cores: normalised values.

Cost of casting

1

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0

1

0,91

Full cores

Empty cores

CONCLUDING REMARKSThe following conclusions can be obtained from the analysis of microstructure andmechanical properties of the castings, realised with full and empty cores:� Secondary dendrite arm spacing is comparable in corresponding positions for the two

kinds of castings. The distribution of eutectic silicon particles is generally uniform andglobular.

� On average, UTSs and YSs are inside the expected range of values; A%s should beincreased in the castings realised with empty cores, probably by means of an

optimisation of the heat treatmentparameters. In general the mechanicalproperties of both kinds of castings arecomparable.

� An inverse correlation between UTSand SDAS is obtained; a finermicrostructure always corresponds tohigher UTSs. YS does not seem to bewell correlated to the scale of thedendritic structure.

� The crack crosses the interdendriticeutectic region: cracked eutectic siliconparticles and microshrinkage and gasporosities can be seen on the fracturesurfaces. Also brittle intermetallicparticles are identified by means of EDSanalysis.

The results obtained by using the Taikaimethodology reveal that severaladvantages from the use of empty coresinstead of full cores can be obtained. Inparticular, a reduction in the weight ofcores determines lower handling costs,lower emission costs and a lower quantityof sand to dispose of. Moreover, the hotflogging treatment is not necessary toguarantee the required mechanical andmicrostructural properties and can beeliminated. Altogether, a reduction of 9%in the total production costs is evaluated.


ACKNOWLEDGMENTSMany thanks are due to TFC-Galileo in Vaccolino of Lagosanto (Ferrara – Italy), for activecooperation and for supplying aluminum castings and X-ray equipment. The authors alsoexpress their gratitude to Dr. Stefano Succi for his experimental contribution to thisresearch.

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[10] Zhang, D.L., Zheng, L.H., and D.H. StJohn. Effect of a short solution treatmenttime on microstructure and mechanicalproperties of modified Al–7 wt.%Si–0.3 wt.% Mg alloy. J. Light Met., 2(2002), 27-36.

[11] Pedersen, L.. Solution heat treatment ofAlSiMg foundry alloys, PhD thesis,Norwegian University of Science andTechnology (NTNU), Trondheim,(1999).

[12] Brown, R.. Foseco non-Ferrousfoundryman’s handbook. InButterworth-Heinemann (Ed), Aluminiumcasting alloys, Oxford, (1999), 23-45.

[13] Salem S., Sjogren, T., and I.L. Svensson.Variations in microstructure andmechanical properties of cast aluminumEN AC 43100 alloy. MetallurgicalScience and Technology, 25 N.1(2007), 12-22.

[14] Backerud, L. and al.. Solidificationcharacteristics of aluminum alloys.Volume 2: Foundry alloys. InAFS/SKANALUMINIUM (Ed), (1990).

[15] Warmuzek, M.. Aluminium-SiliconCasting Alloys: Atlas ofMicrofractographs, In ASMInternational (Ed), (2004).

[16] Gruzleski, J.E., and B.M. Closset. Thetreatment of liquid aluminum-siliconalloys. In American Foundrymen’sSociety Inc. (Ed), Modification andporosity, Des Plaines, Illinois, (1990),57-73.

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